An equation of the line tangent to y=x³+3x²+2 at its point of inflection

First find the point of inflection. get the first derivative to find the second derivative. when  if you test the values of x to the left and to the right of x=-1 for the second derivative, you will see that the sign of the second derivative changes from negative on the left  to positive on the right; therefore, the inflection point occurs at x=-1.the coordinates of inflection: evaluate the original function at the x-coordinate of the inflection point: so the coordinates of the inflection point:   slope of tangent line at  : evaluate the value of the derivative at : so we have a line with a slope of  with a point . using point-slope form of a line:

The internet will you